6533b839fe1ef96bd12a5cb1
RESEARCH PRODUCT
Fisher Renormalization for Logarithmic Corrections
Ralph KennaChristian Von FerberHsiao-ping Hsusubject
Statistics and ProbabilityPhase transitionLogarithmStatistical Mechanics (cond-mat.stat-mech)Multiplicative functionFOS: Physical sciencesStatistical and Nonlinear PhysicsStatistical mechanicsRenormalizationIdeal (order theory)Statistics Probability and UncertaintyCritical exponentScalingCondensed Matter - Statistical MechanicsMathematical physicsMathematicsdescription
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-10-31 |